1 the inspection of dimensions and geometry of ring foundations on their dynamic stiffness using the cone model

 to anticipate the response of a foundation to seismic excitations including earthquakes and machinery loading it is essential to have at hand the dynamic stiffness of the foundation as a component of the impedance based on the geometry of the foundation and the site soil. different types of foundations may be investigated among which ring foundations are of observed in this paper. a typical range of ring foundations has been inspected with the cone model propagation of seismic waves and dynamic stiffness coefficients under a covering range of frequencies for all degrees of freedom have been calculated and compared. for indicated amounts of increase in dimension ratios results show a tendency to converge and as the frequency goes up dynamic stiffness decreases. a convergence threshold equal to 0.4 to 0.8 for dimension ratio was achieved for constant-width foundations which can serve as the upper limit for them to remain dynamically stiff enough when induced by earthquakes. for constant-outer-radii footings the threshold serves a limit of which if the dimension ratio exceeds the rocking stiffness does not reveal noticeable change although torsional stiffness drops drastically. diagrams for comparison of the results are presented.